Healthcare analytics 5. With much acclaim, you have written a machine learning-b

Question

Healthcare analytics 5. With much acclaim, you have written a machine learning-based classifier which diagnoses a particular disease state. Given a person who has the disease, the probability that the classifier will fail to reveal the disease is 0.06. Given a person who does not have the disease, the classifier will correctly identify that the person does not have the disease with probability 0.91 If someone has the disease, what is the probability that the classifier will identify thta person as having the disease? Suppose three unrelated individuals who do not have the disease are classified by your algorithm. What is the probability that at least one of the three individuals will be identified by your classifier as having the disease? In a particular area of a particular country, 17% of the population suffers from this disease. If a random person from this area is tested and and the results indicate that the person has the disease, what is the chance the the person actually has the disease?

Explanation / Answer

Ans:

Fail to reveal=negative

Reveal=positive

P(negative/desease)=0.06

(negative/not desease)=0.92

1)P(positive/desease)=1-0.06=0.94

2)P(positive/not desease)=1-0.92=0.08

P(atleast one of three will be identified by classifier to have desease)=1-P(none)=1-0.923=1-0.7787=0.2213

3)P(desease)=0.17

P(not desease)=1-0.17=0.83

P(desease/positive)=P(positive/desease)*P(desease)/[P(positive/desease)*P(desease)+P(positive/not desease)*P( not desease)]

=0.94*0.17/[0.94*0.17+0.08*0.83]

=0.1598/[0.1598+0.064]

=0.1598/0.2262

=0.71

P(desease/positive)=0.71

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